# トップPDF Lec1 5 最近の更新履歴 yyasuda's website ### Lec1 5 最近の更新履歴 yyasuda's website

2 Assume that both x and y (where x 6= y) are solutions to the consumer problem B(p, ω). By the convexity of the budget set B(p, ω) we have αx + (1 − α)y ∈ B(p, ω) and, by the strict convexity of %, αx + (1 − α)y ≻ z for all α ∈ (0, 1) and z ∈ B(p, ω), which is a contradiction of x being % optimal in B(p, ω).

11 さらに読み込む ### Final 最近の更新履歴 yyasuda's website

(1) Write the payoff functions π 1 and π 2 (as a function of p 1 and p 2 ). (2) Derive the best response function for each player. (3) Find the pure-strategy Nash equilibrium of this game. (4) Derive the prices (p 1 , p 2 ) that maximize joint-profit, i.e., π 1 + π 2 . ### en 最近の更新履歴 yyasuda's website

Introduction to Market Design and its Applications to School Choice.. Yosuke YASUDA.[r]

84 さらに読み込む ### Midterm 最近の更新履歴 yyasuda's website

5. Focal Point (5 points, bonus!) Choose one course offered in GRIPS in the winter term, and write down the name (do NOT write more than one names!). If the course you choose becomes the most popular answer, you would get 5 points. Otherwise, you would get 0 point. You need not explain the reason why you choose that course. ### PS1 最近の更新履歴 yyasuda's website

(a) Show that the above data satisfy the Weak Axiom of revealed preference. (b) Show that this consumer’s behavior cannot be fully rationalized. Hint: Assume there is some preference relation % that fully rationalizes the above data, and verify that % fails to satisfy transitivity. ### PS1 最近の更新履歴 yyasuda's website

(a) Show that if u(x 1 , x 2 ) and v(x 1 , x 2 ) are both homogeneous of degree r, then s (x 1 , x 2 ) := u(x 1 , x 2 ) + v(x 1 , x 2 ) is also homogeneous of degree r. (b) Show that if u(x 1 , x 2 ) and v(x 1 , x 2 ) are quasi-concave, then m(x 1 , x 2 ) := min{u(x 1 , x 2 ), v(x 1 , x 2 )} is also quasi-concave. ### PQ1 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ### Lec1 最近の更新履歴 yyasuda's website

 【戦略】 個々プレイヤーがとることできる行動  【利得】 起こり得る行動組み合わせに応じた満足度、効用 Q: ゲーム解（予測）はどうやって与えられる？ A: 実はノイマン達は一般的な解を生み出せなかった…

22 さらに読み込む ### Micro1 最近の更新履歴 yyasuda's website

More on Roy’s Identity | もっとロア恒等式 Roy’s identity says that the consumer’s Marshallian demand for good i is simply the ratio of the partial derivatives of indirect utility with respect to p i and ω after a sign change.

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“Soon after Nash ’s work, game-theoretic models began to be used in economic theory and political science,. and psychologists began studying how human subjects behave in experimental [r]

26 さらに読み込む ### PracticeF 最近の更新履歴 yyasuda's website

A function f (x) is homothetic if f (x) = g(h(x)) where g is a strictly increasing function and h is a function which is homogeneous of degree 1. Suppose preferences can be represented by a homothetic utility function. Then, show the followings. (a) The marginal rate of substitution between any two goods depends only on the ratio of the demands consumed. That is M RS ij is identical whenever x x j i takes ### Final1 14 最近の更新履歴 yyasuda's website

(b) Does this production function display increasing, constant, or decreasing re- turns to scale? Explain why. (c) Formulate the cost minimization problem (you may denote a target output level by y). Then, solve it and derive the (minimum) cost function, c(w 1 , w 2 , y). ### Final1 12 最近の更新履歴 yyasuda's website

Suppose that the decision maker’s preferences under uncertainty are described by the vNM utility function, u(x) = √ x. (a) Is the decision maker risk-averse, risk-neutral, or risk-loving? Explain why. (b) Calculate the absolute risk aversion and the relative risk aversion, respectively. ### Final1 13 最近の更新履歴 yyasuda's website

6. General Equilibrium (30 points) Consider a production economy with two individuals, Ann (A) and Bob (B), and two goods, leisure x 1 and a consumption good x 2 . Ann and Bob have equal en- dowments of time (= ω 1 ) to be allocated between leisure and work, so the total ### Midterm1 14 最近の更新履歴 yyasuda's website

(a) Suppose % is represented by utility function u(·). Then, u(·) is quasi-concave IF AND ONLY IF % is convex. (b) Marshallian demand function is ALWAYS weakly decreasing in its own price. (c) Lagrange’s method ALWAYS derives optimal solutions for any optimization ### Lec2 1 最近の更新履歴 yyasuda's website

vNM Utility Function (1) Note the function U is a utility function representing the preferences on L(S) while v is a utility function defined over S, which is the building block for the construction of U (p). We refer to v as a vNM (Von Neumann-Morgenstern) utility function.

15 さらに読み込む ### PS2 1 最近の更新履歴 yyasuda's website

not have any Nash equilibrium, including mixed strategy equilibrium. 5. Question 5 (6 points, Review) A crime is observed by a group of n people. Each person would like the police to be informed but prefers that someone else make the phone call. They choose either “call” or “not” independently and simultaneously. A person receives 0 payoff if no one calls. If someone (including herself) makes a call, she receives v while making a call costs c. We assume v > c so that each person has an incentive to call if no one else will call. ### PracticeM 最近の更新履歴 yyasuda's website

Consider a consumer problem. Suppose that a choice function x(p; !) satis…es Walras’s law and WA. Then, show that x(p; !) is homogeneous of degree zero. 6. Lagrange’s Method You have two …nal exams upcoming, Mathematics (M) and Japanese (J), and have to decide how to allocate your time to study each subject. After eating, sleeping, exercising, and maintaining some human contact, you will have T hours each day in which to study for your exams. You have …gured out that your grade point average (G) from your two courses takes the form ### PS1 最近の更新履歴 yyasuda's website

with x = (y, z) where y is a scalar, z is an n-dimensional consumption vector, and V (·) is a real valued function. The consumption set X = R n +1 + . (a) Show that if V is concave, U is quasi-concave. (b) Show that if U is quasi-concave, V is concave. 5. Question 5 (4 points) ### PQ1 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]